Graph spectra in Computer Science

• Published in: Linear algebra and its applications Vol. 434; no. 6; pp. 1545 - 1562
• Main Authors: CVETKOVIC, Dragoš, SIMIC, Slobodan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.03.2011; Elsevier
• Subjects: Algebra; Applications; Applied sciences; Combinatorics; Combinatorics. Ordered structures; Communication technology; Complex networks; Computer Science; Computer science; control theory; systems; Exact sciences and technology; Graph spectra; Graph theory; Information retrieval. Graph; Information technology; Internet; Linear and multilinear algebra, matrix theory; Mathematics; Sciences and techniques of general use; Theoretical computing; 68M07; 68U10; Graph spectra; 05C50; Applications; Graph theory; Communication technology; Information technology; 15A18; 15A51; 81P68; Computer Science; Complex networks; 65F15; Internet; 68R10; 68P20; Modeling; Spectrum; Multiprocessor; Database; Eigenvalue problem; Computer vision; Statistical analysis; Probabilistic approach; Stochastic matrix; Eigenvector; Cubic graph; Data processing
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.11.035

In this paper, we shall give a survey of applications of the theory of graph spectra to Computer Science. Eigenvalues and eigenvectors of several graph matrices appear in numerous papers on various subjects relevant to information and communication technologies. In particular, we survey applications in modeling and searching Internet, in computer vision, data mining, multiprocessor systems, statistical databases, and in several other areas. Some related new mathematical results are included together with several comments on perspectives for future research. In particular, we claim that balanced subdivisions of cubic graphs are good models for virus resistent computer networks and point out some advantages in using integral graphs as multiprocessor interconnection networks.